Self-interference occurs in a high-bandwidth wireless communication network when radio frequency (RF) energy transmitted along one link in a network interferes with the reception of data on another link of the network. This self-interference problem has been addressed in terrestrial communication networks such as mobile telephones, where a cell and cluster network configuration is employed. However, this simple solution does not work well for networks with airborne nodes.
Terrestrial mobile networks (such as the public cellular telephone network) keep track of the location of mobile stations and their emissions and predict or detect significant changes in the environment and thus are able to respond before network conditions create serious self-interference problems. In some networks, such as the cellular telephone network, the distance between base stations is uniform, or at least unchanging. In addition, most surface-to-surface transmission paths are multipath transmission paths rather than line-of-sight, and are thus subject to an RF intensity drop-off proportional to the fourth power of distance. With uniform cell sizes and surface-to-surface multipath transmission paths, a lower bound to the carrier-to-interference ratio in network links can be guaranteed. Thus, even where there are large numbers of emitters in densely populated areas, the carrier-to-interference ratio of cellular telephone networks is bounded so that self-interference does not cripple the network. On the other hand, in networks with airborne emitters, transmission paths are line-of-sight and the intensity of emissions drops only as the square of distance, i.e., as 1/R2.
Let us assume that omnidirectional RF emitters are distributed with uniform density in an infinite, two-dimensional plane. Further assume that each emitter sends to receivers (for example, base stations in a cellular network) as far away as R0, so that a minimum distance between emitters is 2R0. Thus, the average density of emitters on the plane is approximately u=1/(πR02). At distance R0, the average intensity of each emitter is I0.
In the case of multipath communication paths, where intensity drops as the fourth power of distance, it can be shown that an upper bound for the interference level at each base station is I0/4. At other locations, it can be shown that the interference level is also bounded, albeit at a different, finite value. Thus, the interference level in a terrestrial network is bounded even though there are an infinite number of emitters at distances out to infinity under the above set of assumptions.
On the other hand, If it is assumed that the transmission paths in the plane are elevated above the earth sufficiently such that the communication paths are line of sight, it can be shown that the interference level at the location of an emitter is infinite, if it is assumed that there are an infinite number of emitters at distances out to infinity. More practically, it can be shown that the ratio of interference Ii to carrier I0 is the same as the ratio of the distance of a farthest emitter xmax to R0. This indicates that frequency reuse methods that work well in a terrestrial environment will not work well in an airborne RF environment.
Real airborne network nodes are not restricted to a two-dimensional plane. If it is assumed that emitters are distributed in a three-dimensional space, the power emitted by each emitter is still Pe=4πI0R02, but the volumetric power density ρp in three dimensions is ρp=4πI0R02/(4πR03/3)=3 I0/R0. The interference intensity at the location of an emitter is approximated by integrating over a three-dimensional spherical volume and can be shown to be Ii=3 I0(xmax−2R0)/R0. This value is infinite when xmax is infinite. In cases in which xmax is finite but much larger than 2R0, the interference intensity Ii approaches 3 I0xmax/R0, which is three times as bad as the two-dimensional case.
Self-interference levels in real airborne networks lie somewhere between the two-dimensional and three-dimensional airborne models, because movement of airplanes in the vertical direction is much more limited than movement in the horizontal direction. Thus, compact networks may encounter interference that scales more like the three dimensional airborne model, whereas more sparsely populated areas may experience interference that scales more like the two-dimensional model. As a result, more compact airborne networks may experience approximately three times the interference level of a more sparsely populated network. Although the use of narrow beams would help reduce interference levels in either case, the effect of the narrow beams would be to reduce interference by a linear scaling factor, not to reduce the order of the scaling laws.